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Chapter 15: Q4P (page 775)

Assuming a normal distribution, find the limitsμ±hfor a 90%confidence interval; for a 95%confidence interval; for a 99%confidence interval. What percent confidence interval isμ±1.3σ?Hints: See Section8, Example3, and Problems,8.7,8.22 and8.23.

Short Answer

Expert verified

The upper and lower limits are mentioned below:

μ±1.645σμ±1.96σμ±2.579σ

And percent confidence interval,

I=82.5%

Step by step solution

01

Given Information

The value of mean and standard deviation.

μ=0σ=1

02

Definition of Binomial Distribution.

The expected value (also known as expectation) is a generalisation of the weighted average in probability theory.

03

Calculate upper and lower limits for total area of 0.9. 

Calculate limits for confidence interval of90%.

h=1.645μ−1.645σμ+1.645σ

04

Calculate upper and lower limits for total area of 0.95. 

Calculate limits for confidence interval of95%.

h=1.96μ−1.96σμ+1.96σ

05

Calculate upper and lower limits for total area of 0.99.

Calculate limits for confidence interval of99%.

h=2.579μ−2.579σμ+2.579σ

06

Calculate percent confidence interval. 

Use conditions,

μ=0σ=1h=1.36μ±1.36σ

Calculate percent confidence interval.

I=82.5%

Hence, the upper and lower limits are mentioned below:

μ±1.645σμ±1.96σμ±2.579σ

And percent confidence interval,

I=82.5%

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Most popular questions from this chapter

(a) There are 3 red and 5 black balls in one box and 6 red and 4 white balls in another. If you pick a box at random, and then pick a ball from it at random, what is the probability that it is red? Black? White? That it is either red or white?

(b) Suppose the first ball selected is red and is not replaced before a second ball

is drawn. What is the probability that the second ball is red also?

(c) If both balls are red, what is the probability that they both came from the same box?

A weighted coin with probability p of coming down heads is tossed three times; x = number of heads minus number of tails.

Set up several non-uniform sample spaces for the problem of three tosses of a coin

(a) A weighted coin hasprobability23 ofcoming up heads and probability13of coming up tails. The coin is tossed twice. Let x = number of heads. Set up the sample space for x and the associated probabilities.

(b) Find x and σ.

(c)If in (a) you know that there was at least one tail, what is the probability that both were tails?

(a) Find the probability that in two tosses of a coin, one is heads and one tails. That in six tosses of a die, all six of the faces show up. That in12tosses of a12 -sided die, all12 faces show up. That in n tosses of an n-sided die, all n faces show up.

(b) The last problem in part (a) is equivalent to finding the probability that, when n balls are distributed at random into n boxes, each box contains exactly one ball. Show that for large n, this is approximatelye−n2πn.
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